derivative of tan^2(xsec^2(x))

Lösung

\frac{d}{d x} (tan^{2} (x) sec^{2} (x))

2 sec^{4} (x) tan (x) + 2 tan^{3} (x) sec^{2} (x)

Schritte zur Lösung

\frac{d}{d x} (tan^{2} (x) sec^{2} (x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = tan^{2} (x), g = sec^{2} (x)

= \frac{d}{d x} (tan^{2} (x)) sec^{2} (x) + \frac{d}{d x} (sec^{2} (x)) tan^{2} (x)

\frac{d}{d x} (tan^{2} (x)) = 2 tan (x) sec^{2} (x)

\frac{d}{d x} (sec^{2} (x)) = 2 sec^{2} (x) tan (x)

= 2 tan (x) sec^{2} (x) sec^{2} (x) + 2 sec^{2} (x) tan (x) tan^{2} (x)

Vereinfache

2 tan (x) sec^{2} (x) sec^{2} (x) + 2 sec^{2} (x) tan (x) tan^{2} (x) : 2 sec^{4} (x) tan (x) + 2 tan^{3} (x) sec^{2} (x)

= 2 sec^{4} (x) tan (x) + 2 tan^{3} (x) sec^{2} (x)

\frac{d}{d x} (3 x + 4)

\int_{0}^{1} 3 (1 - x)^{2} d x

t an g e n t \frac{( 5 ln ( x ) )}{x}

n = 1 \sum \infty 4 (\frac{1}{2})^{n}

\int \frac{( cos ( x ) ) ^{2}}{2} d x